WIND ENERGY SYSTEMS - Cd3wd

Chapter 6—Asynchronous Generators 6–23
parameters.
The leakage inductances L 1 and L 2 should not vary with temperature, frequency, or voltage
if the machine dimensions do not change. The air gap between rotor and stator may change
with temperature, however, which will cause the inductances to change. A decrease in air gap
will cause a decrease in leakage inductance.
The magnetizing inductance L m is a strongly nonlinear function of the operating voltage
V L due to the effects of saturation in the magnetic circuit. In fact, stable operation of this
system is only possible with a nonlinear L m . The variation of L m depends strongly on the
type of steel used in the induction generator.
We obtain L m from a no-load magnetization curve such as those shown in Fig. 12. These
are basically the same curves as the one shown in Fig. 3 for the dc generator except that these
are scaled in per unit quantities. The various per unit relationships were defined in Section
5.4. Each curve is obtained under no load conditions (R L = ∞) so the slip is nearly zero and
the rotor current I 2 is negligible. The magnetizing current flowing through L m is then very
nearly equal to the output current I 1 . The vertical axis is expressed as V L,pu /ω pu , so only one
curve describes operation over a range of frequencies. Strictly speaking, the magnetization
curve should be the airgap voltage V A plotted against I 1 (or I e ) rather than the terminal
voltage V L . A point by point correction can be made to the measured curve of V L versus I 1
by the equation
V A = V L + I 1 (R 1 + jX 1 ) (24)
The magnetization curve will have somewhat different shapes for different steels and manufacturing
techniques used in assembling the generator. These particular curves are for a
Dayton 5-hp three-phase induction motor rated at 230 V line to line and 14.4 A and a Baldor
40-hp three-phase induction motor rated at 460/230 V line to line and 48/96 A. Measured
parameters in per unit for the 5-hp machine were R m = 13, R 1 = 0.075, R 2 = 0.045, and L 1
= L 2 = 0.16. Measured parameters for the 40-hp machine in per unit were R m = 21.8, R 1 =
0.050, R 2 = 0.025, and L 1 = L 2 = 0.091. The 40-hp machine is more efficient than the 5-hp
machine because R m is larger and R 1 and R 2 are smaller, thereby decreasing the loss terms.
We observe that for the 5-hp machine, rated voltage is reached when I 1 is about half the
rated current. A terminal voltage of about 1.15 times the rated voltage is obtained for an I 1
of about 0.8 times the rated current. It should be noted that it is possible for the magnetizing
current to exceed the machine rated current. The magnetizing current needs to be limited
to perhaps 0.75 pu to allow a reasonable current flow to the load without exceeding machine
ratings. This means that the rated voltage should not be exceeded by more than 10 or 15
percent for the 5-hp self-excited generator if overheating is to be avoided.
The 40-hp machine reaches rated voltage when I 1 is about 0.3 of its rated value. A terminal
voltage of 130 percent of rated voltage is reached for an exciting current of only 0.6 of rated
line current. This means the 40-hp machine could be operated at higher voltages than the
Wind Energy Systems by Dr. Gary L. Johnson November 21, 2001